OK, time for a status update.
I took it to the dealer and had them fix the issue (the TSB helped greatly as he service agent stated he'd never seen the problem in the 3 years he'd been working there). They emailed Lexus and explained the situation and that I just bought the car and Lexus told them to offer me a goodwill gesture of 50/50 on parts and labor. The end cost for me was a little less than $500, which I can live with since I got such a phenomenal deal on the car.
It's been around 5 days now and I've been running the AC and the heat and no little white particles! Woohoo!
Lexus of Orlando definitely has me as a future customer because of this experience.